Rewrite as a simplified fraction. ${2.3\overline{75} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 2375.7575...\\ 10x &= 23.7575...\end{align*}}$ Subtracting the two equations, we have: ${990x = 2352}$ ${x = \dfrac{2352}{990}} $ ${x = \dfrac{392}{165}} \text{or} {2 \dfrac{62}{165}}$